Discrete Transparent Boundary Conditions for 1D linear equations (Antoine Tonnoir, University of Rouen)

23.04.2024 14:00 – 15:00

In this work, we consider the problem of constructing Transparent Boundary Conditions (TBCs) for discretised 1D linear evolution equations (such as the heat equation, wave equation or Klein-Gordon equation). TBCs are used to reformulate a problem posed in an unbounded domain into a problem posed in a bounded domain in a way that the solutions of the two problems (in the bounded and unbounded domain) are the same in the bounded domain. At the continuous level, many results are already known and efficient approximations of the TBCs have been developed (see for instance the absorbing boundary conditions for the wave equation). Yet, for the discretised PDE, the construction of TBCs (called D-TBCs for Discrete-TBCs) is less obvious and fewer results exist (see for instance the work of C. Besse, M. Ehrhardt, X. Antoine). In this talk, we will present an original way to compute these D-TBCs for a class of 1D linear PDEs and arbitrary discretisation schemes. Several numerical examples will be shown to illustrate the results.

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique

entrée libre